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Morphing CSE 590 Computational Photography Tamara Berg
Morphing
CSE 590 Computational PhotographyTamara Berg
Announcements
HW3 online after class
Submit facial point locations by Sunday night (March 17)
Final due date for HW extended to April 1
Image Morphing - Women in Art video
http://youtube.com/watch?v=nUDIoN-_Hxs
Morphing = Object Averaging
The aim is to find “an average” between two objects• Not an average of two images of objects…• …but an image of the average object!• How can we make a smooth transition in time?
– Do a “weighted average” over time t
How do we know what the average object looks like?• We haven’t a clue!• But we can often fake something reasonable
– Usually required user/artist input
Idea #1: Cross-Dissolve
Interpolate whole images:Imagehalfway = (1-t)*Image1 + t*image2
This is called cross-dissolve in film industry
But what if the images aren’t aligned?
Idea #2: Align, then cross-disolve
Align first, then cross-dissolve• Alignment using global warp – picture still valid
Dog Averaging
What to do?• Cross-dissolve doesn’t work• Global alignment doesn’t work
– Cannot be done with a global transformation (e.g. affine)• Any ideas?
Feature matching!• Nose to nose, tail to tail, etc.• This is a local (non-parametric) warp
Idea #3: Local warp, then cross-dissolve
Morphing procedure: for every t,1. Find the average shape (the “mean dog”)
• local warping2. Find the average color
• Cross-dissolve the warped images
Local (non-parametric) Image Warping
Need to specify a more detailed warp function• Global warps were functions of a few (2,4,8) parameters• Non-parametric warps u(x,y) and v(x,y) can be defined
independently for every single location x,y!• Once we know vector field u,v we can easily warp each pixel
Image Warping – non-parametricMove control points to specify a spline warpSpline produces a smooth vector field
Warp specification - denseHow can we specify the warp?
Specify corresponding spline control points• interpolate to a complete warping function
But we want to specify only a few points, not a grid
Warp specification - sparseHow can we specify the warp?
Specify corresponding points• interpolate to a complete warping function• How do we do it?
How do we go from feature points to pixels?
Triangular Mesh
1. Input correspondences at key feature points2. Define a triangular mesh over the points
• Same mesh in both images!• Now we have triangle-to-triangle correspondences
TriangulationsA triangulation of set of points in the plane is a partition of the convex hull to triangles whose vertices are the points, and do not contain other points.
There are an exponential number of triangulations of a point set.
An O(n3) Triangulation AlgorithmRepeat until impossible:
• Select two sites.• If the edge connecting them does not intersect previous
edges, keep it.
“Quality” Triangulations
Let (Ti) = (i1, i2 ,.., i3) be the vector of angles in the triangulation T in increasing order:• A triangulation T1 is “better” than T2 if the smallest angle of T1 is larger than the smallest angle of T2
• Delaunay triangulation is the “best” (maximizes the smallest angles)
good bad
Improving a TriangulationIn any convex quadrangle, an edge flip is possible. If this flip improves the triangulation locally, it also improves the global triangulation.
If an edge flip improves the triangulation, the first edge is called “illegal”.
Illegal Edges
Lemma: An edge pq is illegal iff one of its opposite vertices is inside the circle defined by the other three vertices.
Proof: By Thales’ theorem.
Theorem: A Delaunay triangulation does not contain illegal edges.Corollary: A triangle is Delaunay iff the circle through its vertices is
empty of other sites.Corollary: The Delaunay triangulation is not unique if more than
three sites are co-circular.
p
q
Naïve Delaunay Algorithm
Start with an arbitrary triangulation. Flip any illegal edge until no more exist.Could take a long time to terminate.
Delaunay Triangulation by Duality
Draw the dual to the Voronoi diagram by connecting each two neighboring sites in the Voronoi diagram.• The DT may be constructed in O(nlogn) time• This is what Matlab’s delaunay function uses
Triangular Mesh
1. Input correspondences at key feature points2. Define a triangular mesh over the points
• Same mesh in both images!• Now we have triangle-to-triangle correspondences
3. Warp each triangle separately from source to destination• How do we warp a triangle?• 3 points = affine warp!
Example: warping triangles
Given two triangles: ABC and A’B’C’ in 2D (12 numbers) Need to find transform T to transfer all pixels from one to
the other.How can we compute the transformation matrix:
T(x,y)
?
A
B
C A’C’
B’
Source Destination
11001''
yx
fedcba
yx
Image MorphingWe know how to warp one image into the other, but how
do we create a morphing sequence?1. Create an intermediate shape (by interpolation)2. Warp both images towards it3. Cross-dissolve the colors in the newly warped images
Warp interpolationHow do we create an intermediate warp at time t?
• Assume t = [0,1]• Simple linear interpolation of each feature pair• (1-t)*p1+t*p0 for corresponding features p0 and p1
Morphing & matting
Extract foreground first to avoid artifacts in the background
Slide by Durand and Freeman
Summary of morphing1. Define corresponding points2. Define triangulation on points
• Use same triangulation for both images
3. For each t = 0:step:1a. Compute the average shape (weighted average of points)b. For each triangle in the average shape
– Get the affine projection to the corresponding triangles in each image
– For each pixel in the triangle, find the corresponding points in each image and set value to weighted average
c. Save the image as the next frame of the sequence
View Morphing
Steven M. Seitz, Charles R. Dyer
View Morphing: Key Idea
Beier-Neely morph is NOT shape-preserving!• distortions• un-natural
A Shape-Distorting MorphSource: Steven M. Seitz, Charles R. Dyer
Slide credit: Irwin Chiu Hau
View Morphing: Key Idea
View morphing uses 3D shape preserving morph!• no distortions• natural
A morph is 3D shape preserving if the results of twodifferent views represent new views of the same object
A Shape-Distorting MorphSource: Steven M. Seitz, Charles R. Dyer
View morphing fixesthese intermediate
steps!
Slide credit: Irwin Chiu Hau
Why do we care?
View morphing is efficientProduces new views without
• 3D modeling• Taking additional photos
View morphing creates impressive effects• Camera motion• Image morphing
trueSpaceSource: www.caligari.com
Slide credit: Irwin Chiu Hau
Consider parallel views
How to do View Morphing?
View morphing in three steps1. Prewarp two images2. Compute a morph between the
prewarped images3. Postwarp each in between images
produced by the morph
Slide credit: Irwin Chiu Hau
Results
Results
Facial view morphsSource: Steven M. Seitz, Charles R. Dyer
Slide credit: Irwin Chiu Hau
Results
Results
Top: Image MorphBottom: View Morph
Have a good spring break!
